Can someone please explain to me (USING THE EQUATION) why at equilibrium, Co + cY + Io = (1/[1-mpc]) x (C+I)?



Answer:
AE = Co + MPC*Y + Io

In equilibrium: AE = Y (that is, expenditure equals output).

So,

Y = Co + MPC*Y + Io

isolate for Y:

Y - MPC*Y = Co + Io
(1-MPC)*Y = Co + Io
Y = (1/[1-MPC])*(Co + Io)

Thus, using the definition for Y you can see that:

Co + MPC*Y + Io = (1/[1-MPC])*(Co + Io)

which is what you wanted.
Y=C + I + G + C0 + I0 + G0
C0, I0, G0 don´t depend on Y. c=MPC
C=cY All of them can be written as a proportion of Y.
I=iY
G= gY
Y- cY - iY - gY= C0 + I0 +G0
Y(1-c-g-i)=C0+I0+G0
Y= (C0 + I0 + G0) / (1-c-g-i)

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